2023/04/25 by Masoud Kavian, Mohammad Mahdi Mojahedian, Kavian, Masoud +7
Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Information Theory (cs.IT) #Statistical Distribution Estimation and Applications #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2304.12606
openalex publication_date 2023/04/25 · openalex created_date 2023/04/28 · openalex updated_date 2026/07/28
Random binning is a widely used technique in information theory with diverse applications. In this paper, we focus on the output statistics of random binning (OSRB) using the Tsallis divergence Tα. We analyze all values of α∈ (0, ∞)∪\∞\ and consider three scenarios: (i) the binned sequence is generated i.i.d., (ii) the sequence is randomly chosen from an ε-typical set, and (iii) the sequence originates from an ε-typical set and is passed through a non-memoryless virtual channel. Our proofs cover both achievability and converse results. To address the unbounded nature of T_∞, we extend the OSRB framework using Rényi's divergence with order infinity, denoted D_∞. As part of our exploration, we analyze a specific form of Rényi's conditional entropy and its properties. Additionally, we demonstrate the application of this framework in deriving achievability results for the wiretap channel, where Tsallis divergence serves as a security measure. The secure rate we obtain through the OSRB analysis matches the secure capacity for α∈ (0, 2]∪\∞\ and serves as a potential candidate for the secure capacity when α∈ (2, ∞).